1. Field of the Invention
The present invention relates to a method of growing crystal, or more in particular to a method of growing single crystal with doping impurities added thereto.
2. Description of Related Art
Various methods are available for growing single crystal. The Czochralski method (hereinafter referred to as "the CZ method") is an example. FIG. 1 is a schematic cross-sectional view of a conventional apparatus for growing single crystal according to the CZ method.
In FIG. 1, reference numeral 1 designates a crucible arranged in a chamber not shown. The crucible 1 includes a quartz inner case 1b in the shape of bottomed cylinder and an outer case 1a made of graphite fitted on the outside of the inner case 1b. A heater 2 is concentrically arranged on the outside of the crucible 1. The crystal material melted by the heater 2 is filled in the crucible 1 thereby to form a melted layer L. A seed crystal 4 suspended by a pulling wire 5 is immersed in the melted layer L. The seed crystal 4 is rotated while being pulled up, so that the melted material is coagulated at the lower end of the seed crystal 4, thus growing a single crystal 3.
In the case of growing the single crystal 3 by adding doping impurities (hereinafter referred to as "the dopant") in the melted layer L in this manner, the dopant is segregated along the direction of pulling up the single crystal 3 according to the Pfann equation shown by (1). In the process, the electrical resistivity of the single crystal 3 fails to be constant, and the product yield against the standard value of electrical resistivity is limited. EQU Cs=Ke.multidot.Cc(1-fs).sup.ke-1 ( 1)
where ke is the effective segregation coefficient, Cs the dopant concentration in crystal, Cc the dopant concentration in the melted material at the start of pulling up crystal, and fs the crystal pulling ratio (the ratio of crystal weight to the weight of the crystal material used).
The melted layer method is well known for suppressing the segregation of the dopant. FIG. 2 is a schematic cross-sectional view of a conventional single crystal growing apparatus used for the melted layer method. The apparatus shown in the diagram is substantially similar to the one used for the CZ method shown in FIG. 1 except that in the apparatus shown in FIG. 2, the heater 2 is arranged concentrically on the outside of the upper part of the crucible 1. The same component parts in FIG. 2 as those in FIG. 1 are designated by corresponding reference numerals respectively, and will not be described again.
The crucible 1 is filled with a single crystal material. A solid layer S is coagulated upward from the bottom of the crucible 1, and the heater 2 is controlled in such a manner that the solid layer S as a lower layer coexists with the melted layer L as an upper layer in the crucible 1. The seed crystal 4, which is immersed in the melted layer L, is pulled up while melting the solid layer S at a fixed rate thereby to grow the single crystal 3.
This melted layer method is divided into a constant-thickness melted layer method and a variable-thickness melted layer method. The constant-thickness melted layer method is subdivided into two methods. One is a method disclosed in Japanese Patent Application Publication Nos. 34-8242 and 62-880, in which the solid layer S is formed without containing any dopant and is melted while the single crystal 3 is pulled up, and the amount of the dopant induced into the single crystal 3 is added continuously to the melted layer L while keeping constant the volume of the melted layer L, thereby maintaining the dopant concentration in the melted material constant. According to the other method, as disclosed in Japanese Patent Application Publication No. 62-880 and Japanese Patent Application Laid-Open No. 63-252989, the solid layer 3 containing the dopant is formed and is melted while pulling up the single crystal 3, and the dopant concentration in the melted material is kept constant by keeping the volume of the melted layer L constant without adding the dopant to the melted layer L while the single crystal 3 is pulled up.
In the variable-thickness melted layer method, on the other hand, the solid layer S is formed without containing any dopant and is melted while pulling up the single crystal 3, and the volume of the melted layer L is changed without adding the dopant to the melted layer L while the single crystal 3 is being pulled up, thereby maintaining the dopant concentration in the melted layer L at a fixed level (Japanese Patent Application Publication No. 3-79320).
The principle on which the segregation of the dopant is suppressed by the melted layer method will be explained. FIG. 3 is a one-dimensional model showing the relationship between the dopant concentration and the weight of the single crystal, the melted layer and the solid layer obtained when single crystal is grown by the melted layer method. The abscissa represents the phase ratio coordinate. It is assumed that the dopant has completely mixed in the melted material so that the dopant concentration in the melted material is uniform and there is no diffusion in the solid.
The starting condition of pulling up the single crystal is shown in FIG. 3(a). Characters fs, f.sub.L and fp designate the ratio by weight of the single crystal, the ratio by weight of the melted layer and the ratio by weight of the solid layer, respectively, to the material. Cs, C.sub.L and Cp represent the dopant concentration in the single crystal, the melted layer and the solid layer, respectively. The total weight Wd of the dopant under this condition is given by equation (2) below. ##EQU1##
FIG. 3(b) shows the single crystal as it is being pulled up. The pulling ratio of the single crystal changes to fs+.DELTA.fs, and the solid layer ratio to fp+.DELTA.fp. In the process, the melted layer ratio is f.sub.L -.DELTA.fs-.DELTA.fp, leading to the relation .DELTA.f.sub.L =-.DELTA.fs-.DELTA.fp. The total amount of dopant Wd under this condition is given by equation (4) below. ##EQU2## where Ca.DELTA.f is the amount of dopant added, and Ca the unit amount of dopant added against the crystal pulling ratio.
From equations (2) and (4) and the relation .DELTA.f.sub.L =- .DELTA.fs-.DELTA.fp, equation (5) is obtained. EQU C.sub.s (f.sub.s).DELTA.f.sub.s +C.sub.p (f.sub.p).DELTA.f.sub.p +C.sub.L .DELTA.f.sub.L +.DELTA.C.sub.L f.sub.L =Ca.DELTA.f.sub.s ( 5)
where Cp(1-fp) is represented by Cp(fp) . Equation (5) is expressed in differential form by equation (6). ##EQU3##
Assuming that local growth is established in the growth boundary of a solid, equations (7) and (8) hold in the process of single crystal growth.
Dopant concentration in single crystal EQU Cs=ke.multidot.C.sub.L :.DELTA.fs&gt;0 (7)
Dopant concentration in solid layer EQU Cp=ke.multidot.C.sub.L :.DELTA.fp&gt;0 (8)
In the case where the solid layer is melted (.DELTA.fp&gt;0) while pulling up the single crystal (fs&gt;0), equation (6) may be converted to equations (9A) and (9B) shown below. Equation (9A) indicates the case in which a solid layer exists, and equation (9B) in which the solid layer is melted entirely. ##EQU4##
The melting rate of the solid layer during the process of pulling up the single crystal depends on the internal thermal design of the pulling device. Since the melting rate is normally fixed, however, the melting rate .alpha. is assumed to be given by equation (10). EQU dfp/dfs=-.alpha.&lt;0 (10)
Under this condition, the solid layer ratio fp and the melted layer ratio f.sub.L are expressed respectively as EQU Solid layer ratio fp=fp.sub.0 -.alpha..multidot.fs (11)
(fp.sub.0 : solid layer ratio at the start of pulling the single crystal), and ##EQU5## Equation (13) is obtained from equation (12). ##EQU6## Equation (14A) and (14B) are introduced from equations (9) and (13) ##EQU7##
Equation (14A) shows the case in which a solid layer exists, and equation (14B) the condition after the solid layer is completely melted, which describes the dopant concentration in the melted material.
Single crystal is grown according to the melted layer method either by containing the dopant in the solid layer or by preventing the dopant from being contained in the solid layer.
First, in the method having no dopant contained in the solid layer, Cp=0, and therefore equation (14A) is replaced by equation (15) ##EQU8##
The condition required to prevent segregation of dopant is dC.sub.L /dfs=0. Therefore, equation (16) is introduced from equation (15). EQU C.sub.L (ke-1+.alpha.)=Ca (16)
In the constant-thickness melted layer method, .alpha.=1. Equation (17) shown below thus constitutes the condition for no segregation. EQU Ca=ke.multidot.C.sub.L =ke.multidot.Cb (17)
where Cb is the dopant concentration in the melted material at the start of pulling the crystal.
Since Ca=0 according to the variable-thickness melted layer method, on the other hand, equation (18) below gives the condition for no segregation. EQU .alpha.=1-ke (18)
In either case, the single crystal is segregated according to equation (14B) after the solid layer is completely melted.
In the method with the dopant contained in the solid layer, by contrast, the single crystal material filled in the cruciblel is all melted. The dopant is added to attain uniformity, after which the melted material is coagulated upward from the bottom of the crucible thereby to form a solid layer. Under this condition, the dopant concentration in the solid layer is expressed by equation (19) below. EQU Cp=ke.multidot.Co(1-fp).sup.ke-1 1 ( 19)
where Co is the dopant concentration in the melted material before the solid layer is formed.
The dopant concentration in the melted material at the start of pulling the single crystal is expressed by equation (20). EQU Cb=Co(1-fp.sub.0).sup.ke-1 ( 20)
According to the method in which the dopant is contained in the solid layer, no dopant is added to the melted material and therefore Ca=0. Also, .alpha.=1 in the constant-thickness melted layer method. Equation (21) is thus obtained from equations (19) and (14A). ##EQU9## Equation (21) is modified, leading to equation (22). ##EQU10##
Equation (22) thus introduced is descriptive of the change in dopant concentration according to the constant-thickness melted layer method in which the dopant is contained in the solid layer. This descriptive equation is solved by numerical integration. FIG. 4 is a graph showing the change of dopant concentration in the melted material normalized by the dopant concentration in the melted material at the start of pulling the crystal, as obtained by pulling up the single crystal by the numerical integration. The abscissa represents the single crystal pulling ratio fs, and the ordinate the dopant concentration C.sub.L /Cb normalized by the dopant concentration in the melted material at the start of pulling the crystal. Character A indicates the dopant concentration with the solid layer ratio fp.sub.0 of 0.7 at the start of pulling and the effective segregation coefficient ke of 0.8. Character B designates the change in dopant concentration according to the CZ method. In the case where the dopant is contained in the solid layer according to the constant-thickness melted layer method, it is seen from FIG. 4 that the change in dopant concentration is suppressed as compared with the CZ method although the condition for no segregation is lacking as described above.
In the melted layer methods for growing the single crystal 3 such as silicon by the use of the single crystal growing apparatus shown in FIG. 2, polycrystal is often formed while the single crystal 3 is being pulled up. In the such a case, the single crystal 3 is pulled up through the remelt process of melting the polycrystalized crystal completely into the melted material.
The method in which the dopant is prevented from being contained in the solid layer S according to the melted layer methods through the remelt process (as disclosed in Japanese Patent Application Publication Nos. 34-8242, 62-880 and 3-79320) has the disadvantage that the dopant is undesirably incorporated again into the solid layer S formed as the single crystal 3 is pulled up, thereby making it impossible to obtain a single crystal of the desired dopant concentration.
In the case of the constant-thickness melted layer method for forming the solid layer S with the dopant contained therein, by contrast, the remelt process, if employed, causes no inconvenience since the solid layer S formed when the single crystal 3 is pulled up again assumes a state substantially similar to the initial solid layer S.
Nevertheless, according to the constant-thickness melted layer method in which the solid layer S is formed with the dopant contained therein, the concentration change by the pulling up of the single crystal increases with the decrease in the effective segregation coefficient ke below unity. FIG. 5 is a graph showing the change of the dopant concentration in the melted material with the pulling up of the single crystal when the single crystal is grown by the constant-thickness melted layer method with the solid layer containing the dopant. The abscissa represents the pulling ratio of the single crystal, and the ordinate the dopant concentration C.sub.L /Cb of the melted material while the single crystal is being pulled up as against the dopant concentration in the melted material at the start of pulling up. In FIG. 5, character A designates the change in dopant concentration for the solid layer ratio fp.sub.0 of 0.7 at the start of pulling and the effective segregation coefficient ke of 0.8 in equation (22), and character C the change in dopant concentration for the solid layer ratio fP.sub.0 of 0.7 at the start of pulling and the effective segregation coefficient ke of 0.35.
As obvious from the graph, the dopant concentration change C is greater than the dopant concentration change A. It will therefore be seen that the change in dopant concentration in the melted material with the puling up of the single crystal increases according as the effective segregation coefficient ke decreases below unity. In the case where the change in dopant concentration in the melted material is considerable, as in the case described above, the dopant concentration of the growing single crystal undergoes a change, thereby leading to the problem that a single crystal of the desired electrical resistivity is not obtainable as the single crystal is pulled up.
As shown in FIG. 2, since the silicon melted material is filled in the quartz inner case 1b of the crucible 1, part of the quartz (SiO.sub.2) in contact with the melted material is diffused into the melted layer L. The quartz thus diffused into the melted layer L reacts with the melted material, and the resulting material is partly gasified into silicon oxide, which may reach and attach in the form of solid silicon to the outer wall of the outer case 1a of the crucible 1. In the case where the oxide reaches the heater 2 of resistance heating type made of graphite, on the other hand, CO gas is generated as a result of reaction with graphite and acts to deform the heater 2.
The same silicon single crystal may alternatively be grown under different heating powers of the heater 2 by regulating the heat-insulating material of the heat shield arranged outside of the heater 2 in order to adjust the other qualities required of a single crystal including the oxygen concentration.
In the case where the surface of the heater 2 or the crucible 1 undergoes a secular variation or the single crystal is grown under different heating powers of the heater, as described above, the solid layer ratio at the start of pulling fp.sub.0 is subjected to variations and the desired solid layer ratio fp.sub.0 cannot be obtained even when other conditions for pulling up the crystal remain unchanged. To the extent that the solid layer ratio fp.sub.0 is varied at the start of pulling, the dopant concentration in the melted layer L undergoes variations correspondingly. Assuming that phosphorus is added as a dopant with the desired solid layer ratio fp.sub.0 of 0.5 at the start of pulling and the actual solid layer ratio fp.sub.0 of 0.55 at the start of pulling, for instance, the dopant concentration in the melted layer L is 1.07 times larger than the desired value.
In this way, variations in the solid layer ratio at the start of pulling fp.sub.0 causes variations in dopant concentration in the melted layer L and hence variations in the electrical resistivity of a grown single crystal. As a result, the problem of a reduced yield of the single crystal is posed.